What is expand xy*(1-x-y)^2 ?

The solution to expand xy*(1-x-y)^2 is 2x^2y^2-2x^2y+x^3y-2xy^2+xy^3+xy

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expand xy*(1-x-y)^2

expand

x y \cdot (1 - x - y)^{2}

2 x^{2} y^{2} - 2 x^{2} y + x^{3} y - 2 x y^{2} + x y^{3} + x y

Solution steps

x y (1 - x - y)^{2}

(1 - x - y)^{2} = 2 x y - 2 x + x^{2} - 2 y + y^{2} + 1

= x y (x^{2} + 2 x y - 2 x + y^{2} + 1 - 2 y)

Distribute parentheses

= x y \cdot 2 x y + x y (- 2 x) + x y x^{2} + x y (- 2 y) + x y y^{2} + x y \cdot 1

Apply minus-plus rules

+ (- a) = - a

= 2 xx yy - 2 xx y + x^{2} x y - 2 x yy + x y^{2} y + 1 \cdot x y

Simplify

2 xx yy - 2 xx y + x^{2} x y - 2 x yy + x y^{2} y + 1 \cdot x y : 2 x^{2} y^{2} - 2 x^{2} y + x^{3} y - 2 x y^{2} + x y^{3} + x y

= 2 x^{2} y^{2} - 2 x^{2} y + x^{3} y - 2 x y^{2} + x y^{3} + x y

3 ((2, 0, - 1, 3) - 7 (5, 4, 7, - 1))

2 sin (x) cos (x)

\frac{b ( x - c ) ( x - f )}{( a - c ) ( a - f )}

\frac{( x + 6 ) ^{4}}{4}

(x + 2) (\cdot + 5)

What is expand xy*(1-x-y)^2 ?
The solution to expand xy*(1-x-y)^2 is 2x^2y^2-2x^2y+x^3y-2xy^2+xy^3+xy